We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz image of a thick family of geodesics.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm227-1-6,
author = {Mikhail I. Ostrovskii},
title = {Metric spaces nonembeddable into Banach spaces with the Radon-Nikod\'ym property and thick families of geodesics},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {85-95},
zbl = {06330488},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm227-1-6}
}
Mikhail I. Ostrovskii. Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics. Fundamenta Mathematicae, Tome 227 (2014) pp. 85-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm227-1-6/